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We study the application of polar codes in deletion channels by analyzing thecascade of a binary erasure channel (BEC) and a deletion channel. We show howpolar codes can be used effectively on a BEC with a single deletion, andpropose a list decoding algorithm with a cyclic redundancy check for this case.The decoding complexity is $O(N^2\log N)$, where $N$ is the blocklength of thecode. An important contribution is an optimization of the amount of redundancyadded to minimize the overall error probability. Our theoretical results arecorroborated by numerical simulations which show that the list size can bereduced to one and the original message can be recovered with high probabilityas the length of the code grows.

Polar Coding for the Binary Erasure Channel with Deletions